f$$c$=42$MPa $-$ Bar : $10-15$M

A typical cross$-$section of a prperly reinforced concrete beam is shown in the figure below. The

material properties are summarized below. Use an effective depth of $650$ mm $.$

Given:

$f_y=400$MPa

${}_c=0\mathrm{.}65$

${}_s=0\mathrm{.}85$

$E_s=200000$MPa

a$)$ Is the beam properly reinforced$/$over$-$reinforced$/$ balanced Determine the factored

moment resistance? $(15$ marks$)$

b$)$ Consider the beam section $"$a$)$ "above. However, due to embedded items, the

reinforcing is raised by $65$ mm $,$ such that the effective depth is reduced to $585$ mm

$($Draw the new cross$-$section view$).$ Find the factored moment resistance considering

the new reinforcement layout. $(15$ marks$)$

c$)$ Comment on the effect of the change in reinforcement location on the moment

resistance $(5$ marks$)$

d$)$ Refer to the beam original effective depth. The same contractor reported that, due

to some problems related to batching, the actual $28-$day concrete strength is

reduced by $10\%.$ What is the new $F_c^{\text{'}}?$ Find the factored moment resistance for the

new strength. $(15$ marks$)$

e$)$ What do you believe has a more substantial influence on the magnitude of the

factored moment resistance: a $10\%$ decrease in the concrete strength $($as solved in

part $"$d$)")$ or placement of reinforcement resulting in a $10\%$ decrease in the effective

depth $($as solved in part $"$b$)").$ Why? $(10$ marks$)$